Model averaging with mixed criteria for estimating high quantiles of extreme values: Application to heavy rainfall

TL;DR

This paper proposes a novel model averaging approach combining MLE and LME for estimating high quantiles of extreme rainfall, improving accuracy in small samples and unbounded cases, validated through simulations and real data.

Contribution

It introduces a combined model averaging technique for high quantile estimation, incorporating Bayesian methods to reduce bias and analyzing its theoretical properties.

Findings

Enhanced estimation accuracy demonstrated through simulations.

Application to Korean rainfall data shows practical effectiveness.

Theoretical analysis confirms asymptotic properties of the estimator.

Abstract

Accurately estimating high quantiles beyond the largest observed value is crucial for risk assessment and devising effective adaptation strategies to prevent a greater disaster. The generalized extreme value distribution is widely used for this purpose, with L-moment estimation (LME) and maximum likelihood estimation (MLE) being the primary methods. However, estimating high quantiles with a small sample size becomes challenging when the upper endpoint is unbounded, or equivalently, when there are larger uncertainties involved in extrapolation. This study introduces an improved approach using a model averaging (MA) technique. The proposed method combines MLE and LME to construct candidate submodels and assign weights effectively. The properties of the proposed approach are evaluated through Monte Carlo simulations and an application to maximum daily rainfall data in Korea. In addition, theoretical properties of the MA estimator are examined, including the asymptotic variance with random weights. A surrogate model of MA estimation is also developed and applied for further analysis. Finally, a Bayesian model averaging approach is considered to reduce the estimation bias occurring in the MA methods.